Let \( a=2^{A}, b=2^{B}, \mathrm{C}=2^{C} \) the system of equation...

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Let \( a=2^{A}, b=2^{B}, \mathrm{C}=2^{C} \) the system of equations
\[
\begin{aligned}
a x+b y+(a \alpha+b) z & =0 \\
b x+c y+(b \alpha+c) z & =0 \\
(a \alpha+b) x+(b \alpha+c) y & =0
\end{aligned}
\]
has a non-zero solutions if \( A, B, C \) are in
(a) A.P.
(b) G.P.
(c) H.P.
(d) none of these
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